Modelling sub-canopy landscape-scale shortwave radiation in Eucalyptus forests using a modified Beer-Lambert law combined with airborne LiDAR

In forest systems, direct shortwave radiation (SWR) plays a vital role in fundamental energy and water processes that require high-resolution modelling at the landscape scale. We propose an alternative approach to modelling high resolution, landscape scale, direct SWR transmittance through forest canopies. This approach utilises airborne LiDAR (AB LiDAR) to calibrate a modified Beer-Lambert Law. Over a three-year period, we established the most comprehensive spatial and temporal sub-canopy dataset of 1-minute pyranometer measurements over 31 diverse sites with varying forest densities and age classes in south-eastern Australia. Measuring below canopy SWR at sub-daily and seasonal variations in zenith angle, as well as peak daily and accumulative radiation loads. The modified Beer-Lambert Law (R_bc = R_ace^-kL), utilises path length through the canopy (L) and AB LiDAR as a representation of the sun's beam to measure transmittance (R_bc/R_ac) of above canopy (R_ac) to below canopy (R_bc) radiation; To calculate a site-specific extinction coefficient (k). This approach links the theoretical framework of the Beer-Lambert law with the canopy penetrating properties of AB LiDAR, allowing for large-scale spatial extrapolation of SWR transmittance in forest canopies. This differs from previous studies, which either: apply the Beer-Lambert law or the LiDAR penetrating properties separately, use AB LiDAR to represent the vegetation structure from which a Leaf Area Index (LAI) is calculated and transmittance modelled using specific leaf projection functions, or use computationally intense approaches such as ray tracing. These approaches have limitations as they either require site-specific calibration at the point scale, don’t account for seasonal variations in beam penetration angle, are difficult to parameterise across the landscape, or are too computationally intense to feasibly run at the landscape scale. The proposed model combined with LiDAR calibration addresses these limitations as the path length changes with zenith angle, and the calibration of the extinction using LiDAR allows for landscape-level parameterisation in a computationally friendly workflow. With the expanding availability of AB and spaceborne LiDAR, the linking of the penetrating properties of LiDAR with the theoretical concept of the Beer-Lambert law will allow below canopy direct SWR to be modelled with improved accuracy at large scales over daily and seasonal timespans. This improves our ability to model radiation loading below forest canopies across diverse landscapes and terrains, improving the modelling of hydrological, micro-climate, energy and water processes.